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Title: Homomorphisms and derivations on Banach algebras
Author: Cusack, Julian M.
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 1976
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This thesis is concerned with some problems in three areas of Banach algebra theory. These are dealt with separately in Chapters 2, 3 and 4. Chapter 2 is concerned with certain automatic continuity problems for homomorphisms and derivations on Banach algebras. The main result is that if there exists a discontinuous homomorphism from a Banach algebra onto a semi-prime Banach algebra, or a discontinuous derivation on a semi-prime Banach algebra, then there exists a topologically simple radical Banach algebra. The main result of Chapter 3 is that there are no Jordan derivations which are not also associative derivations on any semi-prime algebra over a field not of characteristic 2. It follows from this that every Jordan derivation on a semi-simple Banach algebra is a derivation, and therefore continuous. The background to Chapter 4 is a theorem which states that if A is a C'-algebra with identity, acted on by a group G of isometric automorphisms in such a way that A is G-abelian, then the mot of G-invariant states of A is a simplex. This was proved by Lanford and Ruelle in connection with the C*-algebra approach to statistical mechanics. Methods are developed to provide an alternative proof of this result and to investigate the possibility of similar results holding in special cases when A is not a C*-algebra.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available